Using the connection between intersection theory on the DeligneMumformd spaces Mg,n and the edge scaling of the GUE matrix model (see [12, 14]), we express the n-point functions for the intersection numbers as n-dimensional error-function-type integrals and also give a derivation of Witten’s KdV equations using the higher Fay identities of Adler, Shiota, and van Moerbeke.